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Quantum Electronics

Stabilisation of emission in the first Stokes component of stimulated Raman scattering in the nonlinear regime

N. I. Shamrov

Published Mar 31, 2000• 4 citations
Publisher

Abstract

Equations of coherent stimulated Raman scattering were solved analytically for samples of length smaller than the wavelength of incident radiation, and numerically for extended media. The energy distribution function of Stokes pulses was determined. Transition from the linear regime of stimulated Raman scattering to the nonlinear regime was studied. The intensity of the first Stokes component was shown to be stable in the case of saturated amplification of spontaneous emission.

DOI
10.1070/qe2000v030n03abeh001696

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Equations of coherent stimulated Raman scattering were solved analytically for samples of length smaller than the wavelength of incident radiation, and numerically for extended media. The energy distribution function of Stokes pulses was determined. Transition from the linear regime of stimulated Raman scattering to the nonlinear regime was studied. The intensity of the first Stokes component was shown to be stable in the case of saturated amplification of spontaneous emission.
An analytic solution is obtained for the equations of resonance coherent SRS by neglecting the population of the final level of the Raman transition for the systems with the active-medium length that is smaller than the wavelength of the incident light. For the extended systems, a numerical solution is obtained. The energy distribution of the Stokes pulses is found. The large-scale (about 100%) fluctuations of the Stokes radiation energy were observed in the case of unsaturated amplified spontaneous emission.
The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
The influence of the scattering matrix elements that are responsible for the amplification of the Stokes and anti-Stokes components on the process of stimulated Raman scattering in the essentially nonstationary regime is analyzed. It is demonstrated that the optimum proportion between the scattering matrix elements, which maximizes the anti-Stokes component, is determined by the ratio between the optical frequencies of the components and the initial proportion between the intensities of the pump and initiating pulses. In the case of the optimum proportion between the scattering matrix elements, the variation in the excitation of a medium compensates the self-induced modulation of gain, and the efficiency of converting the radiation energy into the Stokes and anti-Stokes components increases substantially.
The results of the investigation of Stokes energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump are presented. The pulse-energy distributions and their standard deviations were measured. The comparison of the experimental data with known ones for coherent pump shows the strong difference in the distribution shape and the standard deviation value. This difference is explained as a manifestation of the non-Gaussian (super-Gaussian) statistics in stimulated scattering with a broad-band pump. The results of numerical calculations for statistics of Stokes intensity are in a qualitative agreement with the experimental findings.
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.
A semiclassical model of nonstationary stimulated Raman scattering with account of forward and backward waves of different frequencies is proposed. Equations for the elements of a collective density matrix and electric-field amplitudes are obtained applying the averaging method. It is shown that forward waves are generated by a united polarization component, whereas each of the backward waves is formed by its own component. The description is based on the approximation of small scattering angles and assumes that the quantities considered do not depend on transverse coordinates. The emission dynamics of forward-backward Stokes pulses is investigated both for the linear case and under the strong depletion of pumping and level populations. The domain of applicability of the model of nonstationary forward stimulated Raman scattering is determined.